\newcommand{\evold}[1]{\ensuremath{\mathcal{E}_d^{\mathtt{#1}}}\xspace}
\newcommand{\evols}[1]{\ensuremath{\mathcal{E}_s^{\mathtt{#1}}}\xspace}


%Full evolvability CCS
\newcommand{\evol}[1]{\ensuremath{\mathcal{E}^{\mathtt{#1}}}\xspace}




\newcommand{\OG}{\ensuremath{\mathsf{BA}}\xspace} % bounded adaptation
\newcommand{\LG}{\ensuremath{\mathsf{EA}}\xspace} % eventual adaptation



%separator
\newcommand{\sepr}{ \  \  \mid \ \ }

%operatori
\newcommand{\update}[2]{\widetilde{#1}\{#2\} } % a{P}
\newcommand{\updatebig}[2]{\widetilde{#1}\big\{#2\big\} } % a{P}
\newcommand{\updatebbig}[2]{\widetilde{#1}\bigg\{#2\bigg\} } % a{P}


\newcommand{\component}[2]{#1 [#2]   }  %a[P]
\newcommand{\componentbig}[2]{#1 \bigg[ #2 \bigg]   }  %a[P]
\newcommand{\componentbbig}[2]{#1 \big[ #2 \big]   }  %a[P]

\newcommand{\supd}[2]{\til{#1}^\circ\{#2\} } % a^o {P} subjective
\newcommand{\oupd}[2]{\til{#1}^\bullet\{#2\} } % a^o {P} objective o piena

\newcommand{\scomp}[2]{#1^\circ [#2]}    %a^o[P]
\newcommand{\ocomp}[2]{#1^\bullet [#2]}  %a^o[P]

\newcommand{\tuple}[2]{\langle #1 , #2 \rangle}


\newcommand{\procleq}{\preceq}
\newcommand{\subp}{\ensuremath{\mathsf{sub}}}

%\newcommand{\procleq}{\preceq}
\newcommand{\Comp}{\mathtt{Comp}}
%\newcommand{\subp}{\mathit{Sub}}
\newcommand{\ClSub}{\mathtt{ClSub}}
\newcommand{\nset}[1]{\ensuremath{\mathsf{lab}(#1)}}
\newcommand{\Tree}{\mathsf{Tr}}
\newcommand{\Pred}{\mathsf{Pred}}
\newcommand{\cnames}{\mathsf{apn}}

\newcommand{\barb}[1]{\! \Downarrow_{#1} }
\newcommand{\barbk}[1]{\! \Downarrow_{#1}^k }
\newcommand{\barbw}[1]{\! \Downarrow_{#1}^{\omega} }

\newcommand{\negbarbk}[1]{\rotatebox[origin=c]{270}{$\nRightarrow$}_{#1}^{\hspace{0.2mm}k}}
\newcommand{\negbarbw}[1]{\rotatebox[origin=c]{270}{$\nRightarrow$}_{#1}^{\hspace{0.2mm}\omega}}

\newcommand{\newbarb}[2]{#1 \rotatebox[origin=c]{270}{$\Mapsto$}_{#2}^{\hspace{1mm}k}}

\newcommand{\negbarb}[1]{\neg \Downarrow_{#1}^{ERROR}}


\newcommand{\BC}{{\cal CS}}


\newcommand{\newarro}[1]{\xrightarrow{#1} }
%\newcommand{\newarro}[1]{\shortmid \! \xrightarrow{#1} } %|->
\newcommand{\bigset}[1]{{\cal T}_{#1}}

\newcommand{\Par}{\mathsf{Par}}

\newcommand{\CStr}{\ensuremath{\mathsf{St}}}
\newcommand{\CStrs}{\ensuremath{\mathsf{Sub}_{\mathsf{St}}}}
\newcommand{\rootch}{l}
\newcommand{\dyn}[1]{\llbracket #1 \rrbracket_S^{\mathit{d}}}
\newcommand{\dyns}[2]{\llbracket #1 \rrbracket_{#2}^{\mathit{d}}}


\newcommand{\mmn}[1]{\ensuremath{\mathsf{#1}}}
\newcommand{\mmss}{MMs\xspace}
\newcommand{\mm}{MM\xspace}


\newcommand{\controll}{\ensuremath{\mathrm{\textsc{Control}}}\xspace}

\newcommand{\gar}[1]{G^{\langle#1\rangle}}
\newcommand{\garb}[2]{G_{#2}^{\langle#1\rangle}}


\newcommand{\fillcont}[2]{\ensuremath{#1[#2]}}
\newcommand{\fillcontbig}[2]{\ensuremath{#1\big[#2\big]}}
\newcommand{\fillcontBig}[2]{\ensuremath{#1\Big[#2\Big]}}




\newcommand{\xevol}{\ensuremath{\mathcal{E}^{2}_{\mathsf{RC}}}\xspace}

\newcommand{\mma}{Minsky machine\xspace}
\newcommand{\hide}[1]{}
\newcommand{\hof}{\ensuremath{\textsc{Ho}^{-\mathsf{f}}}\xspace}
\newcommand{\hopf}{\ensuremath{\textsc{HoP}^{-\mathsf{f}}}\xspace}
\newcommand{\hocore}{\ensuremath{\textsc{Hocore}}\xspace}

\newcommand{\rulename}[1]{\textsc{(#1)}}

\newcommand{\linefigure}{\centering\hrulefill\vspace{-4ex}}


\newenvironment{myfigure}[1]{
  \centering\hrulefill\par\vspace{-4ex}
  \begin{figure}[#1]   
   \end{figure}
   \centering\hrulefill\par\vspace{-4ex}}
    
    
    


% Languages with components
\newcommand{\ccs}{\ensuremath{\textsc{CCS}}\xspace}
\newcommand{\comp}[1]{\ensuremath{\mathcal{C}^{\mathtt{#1}}}\xspace}

% 
\newcommand{\wssts}{\ensuremath{\textsc{WSSTS}}\xspace}
\newcommand{\wsstss}{\ensuremath{\textsc{WSSTS}\mathrm{s}}\xspace}

% Notation for definitions
%\newcommand{\numholes}[1]{\ensuremath{\#_{\bullet}(#1)}}
%\newcommand{\numholesb}[1]{\ensuremath{\#_{\bullet}\Big(#1\Big)}}
%\newcommand{\numap}[1]{\ensuremath{\#_{\text{ap}}(#1)}}

\newcommand{\numholes}[1]{\ensuremath{{|}#1{|}_{\bullet}}}
\newcommand{\numap}[1]{\ensuremath{{|}#1{|}_{\mathsf{ap}}}}
\newcommand{\numtap}[1]{\ensuremath{{|}#1{|}_{\mathsf{tap}}}}
\newcommand{\numph}[1]{\ensuremath{{|}#1{|}_{\mathsf{ph}}}}
\newcommand{\numpha}[1]{\ensuremath{{|}#1{|}_{\mathsf{\underline{aph}}}}}

\newcommand{\upd}[1]{\ensuremath{\mathsf{Upd}(#1)}}


\newcommand{\depth}[1]{\ensuremath{\mathsf{depth}(#1)}}
\newcommand{\maxDistance}[1]{\ensuremath{\mathsf{maxDistance}(#1)}}
\newcommand{\maxDist}[2]{\ensuremath{\mathsf{maxDist}_{#1}(#2)}}
\newcommand{\maxDepCom}[1]{\ensuremath{\mathsf{maxDepCom}(#1)}}
\newcommand{\deriv}[1]{\ensuremath{\mathsf{Deriv}(#1)}}

\newcommand{\encoding}[1]{\llbracket #1 \rrbracket}
\newcommand{\pass}[2]{\til{#1} \{ #2 \}}

% Command for context
\newcommand{\fillcon}[2]{\ensuremath{#1\hl{#2}}}

%%% Commands for Petri Nets
\newcommand{\derivv}{\rightarrow}
\newcommand{\derriv}{\Rightarrow}
\newcommand{\nat}{Nat}
%\newcommand{\semm}[2]{[\!\![\!\![#1,#2]\!\!]\!\!]}
\newcommand{\semm}[2]{\{\!\!\{#1,#2\}\!\!\}}
\newcommand{\subb}[1]{\ensuremath{\mathsf{sub}(#1)}}
\newcommand{\possupd}[1]{upd(#1)}
\newcommand{\maxc}[1]{maxClstr(#1)}

\newcommand{\pnr}[2]{\ensuremath{\mathsf{PN}(#1,#2)}}
\newcommand{\pseq}{{\mathcal P}_{seq}}
\newcommand{\ambpaths}{\mathcal A}
\newcommand{\coppia}[2]{\langle #1,#2 \rangle}
\newcommand{\places}[1]{{\mathsf{Places}}(#1)}
\newcommand{\initMark}[1]{{\mathsf{Init}}(#1)}
\newcommand{\transit}[1]{{\mathsf{Trans}}(#1)}
\newcommand{\decc}[2]{\ensuremath{\mathsf{dec}_{#1}(#2)}}


%%% End commands Petri Nets

\pagestyle{plain}

\newtheorem{mynotation}{Convention}[section]
\theoremstyle{plain}

\newcommand{\Ho}[2]{\overline{#1} \langle #2 \rangle}


%%% Height
%\addtolength{\voffset}{-0.1cm} 
%\addtolength{\textheight}{0.2cm} 
%%% Width
%\addtolength{\hoffset}{-0.2cm}
%\addtolength{\textwidth}{0.3cm} 

%\usepackage{hyperref}

\newcommand{\reso}[1]{\ensuremath{C}^{\langle #1 \rangle}}


%% Notation for spatial wsts
%\newcommand{\pb}[1]{\ensuremath{\mathsf{pb}(#1)}}
\newcommand{\mub}[2]{\ensuremath{\mathsf{mub}(#1,#2)}}
\newcommand{\fb}[1]{\ensuremath{\mathsf{b}(#1)}}
\newcommand{\Lo}{{\ensuremath{\mathcal{L}}}\xspace}
\newcommand{\Lmon}{{\ensuremath{\mathcal{L}_0}}\xspace}


\newcommand{\Deriv}{Deriv}